On the validity of the use of Legendre moments in the vicinity of well pronounced resonances

The two body kinetics theorem has been already dealt over the last 90 years. For the calculation of the scattering terms in nuclear reactor simulation, the so called asymptotic approach was commonly used. It assumes that the target nuclide is at rest before the interaction with the neutron and that the nuclide is free (not bound within a molecule, crystal lattice etc). Extensive studies were performed to include the impact of the chemical binding of light isotopes on the scattering process. However, for heavy isotopes the above mentioned ''target at rest'' approximation is still commonly used. Strictly speaking, the effect of the temperature and existence of energy dependent cross sections were neglected as far as the secondary energy distribution is concerned. Consequently, the interpretation of the angular distribution via Legendre moments for the asymptotic approximation could have been realized with one or few higher moments. In this study the calculation of the temperature and energy dependent (Doppler broadened) scattering kernel by means of higher Legendre moments is presented. In this study, it is shown that if the resonance dependent kernel is introduced, the number of higher moments for the angular description of the scattering in the vicinity of the main resonances of 238U is by far higher and due to the numerical complexities might not be usable for practical core simulation. (orig.)